We study relativistic self-dual Chern-Simons-Higgs systems in the presence of uniform background fields that explicitly break CTP. A rich, but discrete vacuum structure is found when the gauge symmetry is spontaneously broken, while the symmetric phase can have an infinite vacuum degeneracy at tree level. The latter is due to the proliferation of neutral solitonic states that cost zero energy. Various novel self-dual solitons, such as these, are found in both the symmetric and the asymmetric phases. Also by considering a similar system on a two-sphere and the subsequent large sphere limit, we isolate sensible and finite expressions for the conserved angular and linear momenta, which satisfy anomalous commutation relations. We conclude with a few remarks on unresolved issues.

LaTeX, 20 pages, 4 uuencoded figures included.